Page 367 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes • No statistic can be guaranteed to provide a close value of the parameter on each and every occasion,
and for every sample. Therefore, one has to be content with formulating a rule/method which
provides good results in the long run or which has a high probability of success.
• Incidentally, while the method or rule of estimation is called an estimator like sample mean,
the value which the method or rule gives in a particular case is called an estimate.
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• An estimator θ is said be unbiased estimator of the population parameter θ if the mean of the
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sampling distribution of the estimator θ is equal to the corresponding population parameter θ .
• An estimator is said to be consistent if the estimator approaches the population parameter as
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the sample size increases. In other words, an estimator θ is said to be consistent estimator of
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the population parameter θ , if the probability that θ approaches θ is 1 an n becomes large
and larger.
• Efficiency is a relative term. Efficiency of an estimator is generally defined by comparing it
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with another estimator. Let us to take two unbiased estimators θ and θ . The estimator θ is
2
1
1
ˆ
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called an efficient estimator of θ if the variance of θ is less than the variance of θ .
2
1
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• The last property that a good estimator should possess is sufficiency. An estimator θ is said to
be a ‘sufficient estimator’ of a parameter θ if it contains all the informations in the sample
regarding the parameter. In other words, a sufficient estimator utilises all informations that the
given sample can furnish about the population. Sample means X is said to be a sufficient
estimator of the population mean.
28.5 Key-Words
1. Deviation scores : Data in which the mean has been subtracted from each observation.
2. Descriptive statistics : Statistics which describe the sample data without drawing inferences
about the larger population.
28.6 Review Questions

1. What is Estimation ? How many types of estimates are possible ?
2. Explain the properties of a good estimator ?
3. What do you understand by point estimator ?
4. Discuss the application of point estimation.
5. Distinguish between consistency and efficiency.
Answers: Self-Assessment
1. (i) Point estimate, interval estimate (ii) Mean (iii) Population

(iv) Parameter (v) θ .
28.7 Further Readings

1. Elementary Statistical Methods; SP. Gupta, Sultan Chand & Sons,
New Delhi - 110002.
2. Statistical Methods — An Introductory Text; Jyoti Prasad Medhi, New Age
International Publishers, New Delhi - 110002.
3. Statistics; E. Narayanan Nadar, PHI Learning Private Limied, New Delhi - 110012.
4. Quantitative Methods—Theory and Applications; J.K. Sharma, Macmillan
Publishers India Ltd., New Delhi - 110002.

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